We’ve been through turbulent times again this year. A year ago we were in the midst of a huge spike in cases of the omicron variant and heading for another Christmas badly affected by the pandemic.
Covid is not over – we seem to be finding a way to live with it now – but the challenges this year are perhaps even more daunting. We’d all hoped that by now that further education would be on the road to recovery and that rising funding would start to make life a little bit easier.
With runaway inflation, and the energy crisis, that’s far from the case. The impact is all too evident; with the chief inspector at Ofsted warning this week that quality in colleges is suffering from a lack of skilled staff which in turn is driven by inadequate funding resulting in low pay.
We’ve also seen Education Policy Institute analysis showing that the disadvantage gap in education has widened over the last few years.
To add to the gloomy picture, the Institute for Fiscal Studies repeated their analysis from the last few years showing the dire state of FE funding and the Public Accounts Committee published another timely report which underscores the problem.
We all know the funding picture now after more than a decade of austerity is unsustainable and it is obvious action is needed, but the government seems unwilling to act for colleges, having seemingly deemed that increased funding for schools was a bigger vote-winner in the Autumn Statement.
After five education secretaries, three skills ministers, four chancellors and three prime ministers this year, we have ministers now at the top table in Sanctuary Buildings – Gillian Keegan and Rob Halfon – who know us well. We have to hope that their understanding and commitment to FE and colleges can help them secure funding from Treasury.
We don’t want any more warm words about skills and the importance to productivity, economic growth and levelling up – those words don’t help, they even make it all feel worse. What we need to see is proper, sustained investment and a more stable period for colleges to get on with meeting the needs in their communities.
Unfortunately, we are asking for more funding at the same time as the Chancellor is planning a new set of severe public sector cuts from 2024/25.
Our challenge is to show that funding for colleges is an investment with strong returns for the economy and for the Treasury. We will need to remind the Chancellor of his own words in presenting the Autumn Statement that to “be pro-education is to be pro-growth”.
For us at AoC, and for college leaders we are determined to be louder, bolder and more combative in our campaigning and influencing.
We’ll not be doing that alone, as our Future Skills Coalition shows. That collaboration with the Association of Employment and Learning Providers (AELP) and City & Guilds has already started to bring other organisations on board to form a wider coalition of voices which we believe will make more of an impact where it matters.
We are also urging college leaders to step up again and be part of the fight. Their work in engaging MPs, mobilising the employers they work with, and their students can have a big impact when amplified across the country at key points in the year.
Redoubling our efforts now is the right thing to do, as every other sector will also be scrambling to make the case for better funding amid fiscal tightening, especially in the run-up to a general election within two years.
It can feel exhausting to keep having to make the same arguments, especially when the case for a properly funded skills system could not be clearer.
It is vital though to make our case strongly because it is the persistent voices – and the loudest voices – which cut through.
We need now to fight for our sector, to fight clever, to take a united front to make the case for better skills funding. I am optimistic that we will do that and hopeful that it will reap rewards.
Plans to integrate mandatory qualifications with final assessments in apprenticeships have been put to the sector for a 10-week consultation.
The Institute for Apprenticeships and Technical Education (IfATE) has published its proposals to make mandatory professional qualifications work “seamlessly” with the end point assessments (EPAs) and eliminate some of the current problems in the system.
Currently, an apprenticeship doesn’t end until the end point assessment has been completed, but for many apprenticeships such as electrician or adult care worker, a professional qualification to work in their industry are also required. Those qualifications are often completed before the EPA.
IfATE reckons around 40 per cent of apprenticeships mandate at least one qualification.
But it says there is evidence that learners leave their apprenticeship after gaining the qualification and before EPA, meaning there is no formal record of their knowledge, skills and behaviours.
It has also found that assessment in the professional qualification may also duplicate parts of the EPA, resulting in “overassessment of learners and inefficiency”.
IfATE’s new proposals aim to integrate at least one of a qualification’s assessments with the EPA, to be conducted after a learner reaches gateway as part of the main EPA. That would ensure learners complete their whole programme at the end of the apprenticeships and strip out duplication.
It will require end point assessment organisations (EPAOs) to make clear in their marking criteria where the grade boundaries will be in the integrated assessment to pass EPA.
In addition, the proposals will require employers to submit a rationale and supporting evidence that a professional qualification is needed to prevent disadvantage in the labour market for learners.
It also wants to ensure “that the qualifications are necessary, because an apprentice would struggle to get a job or progress after finishing the apprenticeship, without them”.
A consultation has launched this week for the sector to share feedback, closing on February 17.
Sam Callear, IfATE deputy director for policy and new concepts, said the proposals are based on its experience in developing apprenticeships over the last few years, as well as feedback from employers, apprentices, providers and EPAOs, accepting that qualifications and EPAs “haven’t always worked together as well as they could”.
“We think we can improve the balance and relationship between the study and assessment needed to achieve these specific qualifications and the study and assessment that is needed as part of the apprenticeship,” he added.
Responses to the consultation can be submitted online here.
Jane Hickie, chief executive of the Association of Employment and Learning Providers welcomed the consultation. Writing in the organisation’s weekly newsletter, she said: “Similar to the approach with degree apprenticeships, this is to reduce duplicate assessments and help to stop apprentices leaving early without completing EPA.
“This would be a win all round for the apprenticeship brand and drive higher success rates.”
Apprenticeship drop-outs have been a key problem for the sector, with figures for last year indicating that 47 per cent – nearly half – of apprentices failed to see their course through to the end.
Complex Covid-19 assessment adaptations, poor communication from awarding organisations and an influx of inexperienced exams officers were to blame for “unacceptable” delays to thousands of level 2 and 3 results this summer, two new reports suggest.
The two awarding organisations at the centre of the controversy – Pearson and OCR – have today published their own reports on the errors.
They have pledged to introduce check points with colleges, schools and providers during term time to establish any missing data earlier, and invest in more training for teachers and exam staff through complex systems.
Pearson’s report says it will also release results under embargo around a week before the results are released, rather than 24 hours before.
OCR meanwhile, which had just under 11,000 delayed results, has promised to review risk logs for Cambridge Technicals more regularly and conduct a review of staff expertise, as well as bolster relationships with schools and colleges.
The earlier results, check points, training and improved communication measures were announced by Ofqual this morning.
Both Pearson and OCR will also be represented on a new taskforce of sector leaders to implement new measures in time for summer 2023.
A Pearson spokesperson said: “It was unacceptable that some students did not receive their results when they were expecting them this summer, and we apologise for Pearson’s role in this.
“We are part of Ofqual’s new 2023 VTQ taskforce and look forward to working with Ofqual and the wider education community on improvements for the future.”
OCR chief executive Jill Duffy said she accepted in full the findings of its report, carried out by OCR staff and overseen by the University of Cambridge’s Professor Graham Virgo.
She added: “It pinpoints what went wrong this summer, and it takes a pragmatic approach to identifying improvements that will not only prevent a recurrence, but improve the wider experience for students, parents, schools and colleges.”
Pearson was at the centre of the storm in August as thousands of BTEC students reported showing up on results day to find an empty box where their final grade should have been.
The awarding body’s review, led by former Education and Training Foundation chief executive David Russell, describes how missing or incomplete data from colleges and schools on students’ exams and coursework results led to most of the delays.
Administration processes were “more complex than usual” because students completing BTECs will have experienced a range of adaptations to their assessments due to the pandemic – all of which came with additional requirements on teachers and centres.
Pearson also cite survey evidence from the National Association of Examinations Officers stating that 22 per cent of exams officers were new in post in 2022, suggesting a large proportion of the exams workforce wasn’t experienced enough to handle “complex data collation processes”.
Pearson has said that 55 per cent of the delayed results came from just 7 per cent of its centres, which those impacted most tending to offer large numbers of BTEC programmes or have a large number of sites.
Jill Duffy
One of the criticisms of awarding organisations at the time was that errors in data supplied by centres was not spotted and fixed prior to results day.
To this, Pearson, which had just under 10,000 delayed results in England, said: “We alerted every centre where our system reconciliations showed unit grades were missing and provided reports listing all students with incomplete results so that schools or colleges could identify gaps.”
However the report added: “Our findings show there are areas for improvement in how we communicate about missing data with schools and colleges, and it is clear that we need to check more carefully that information and data requests have been received and are being actioned.”
OCR meanwhile said it was not apparent there were issues until results day itself, when it began fielding calls from schools and colleges and prompted a hasty mobilisation of staff to process results. It said that most delayed results were able to be provided within a week but “some complex cases took until 7 September”.
It said that in “almost all cases of delayed results, OCR had not received the full details needed to process qualifications from schools and colleges for those students”.
The report said that the Covid adaptations – which included teacher-assessed grades, reduced assessment in coursework and allowance of assessed grades for students who couldn’t sit exams – in conjunction with a “significant increase in missing and incomplete results” was behind the issue.
Its report said the problem exposed a need for greater data sharing between OCR, schools, colleges and UCAS than existing processes delivered, and guidance to schools and colleges either did not reach or wasn’t understood sufficiently by those who needed to know how to handle complex processes.
The two organisations will now feed into the new task force to work on implementing changes for 2023, as well as look at potential tweaks beyond to create as efficient a system as possible
A review by exams regulator Ofqual has found that nearly 21,000 students were affected by BTEC and CTEC results delays last summer, more than 55 per cent more than was previously thought.
Regulators have today published an action plan for 2023 vocational and technical qualification results, which they hope will prevent a repeat of this year’s blunder, but more time is needed to determine the cause of the delays and the appropriate sanctions on awarding bodies.
Ofqual will introduce a “hard deadline” for vocational qualification results next summer and form a taskforce with sector chiefs to prevent results delays seen this year with BTEC and Cambridge Technicals from happening again.
It comes as new data reveals that more students were affected by the summer problems than first thought.
The exams watchdog today announced a five-point plan to ensure problems arising in this summer’s exams, which left thousands of students on Pearson BTEC and OCR CTEC courses waiting for results way beyond level 3 results day in August.
Figures from October’s education select committee scrutiny of the issue indicated that there had been around 13,500 results delayed – 7,000 level 2 BTECs, , 3,300 level 3 BTECs and 3,200 CTECs.
But figures released by Ofqual today revealed it was around 21,000 results in total – 12,346 level 3 results and 8,573 level 2 results. That was across 1,550 schools, colleges and other centres.
Ofqual’s chief regulator Dr Jo Saxton told FE Week that more work is continuing on investigating the root causes of the delays, and said it was too early to talk about any possible sanctions, but unveiled five measures to begin in 2023 to ensure the same issues do not arise next summer.
That includes a hard deadline for vocational and technical qualification results, likely to be a week before the main level 3 results deadline for general qualifications like A-levels, but to be finalised in consultation with the sector to ensure it is the right timing.
In addition, a taskforce will be formed of “key senior sector leaders of those who were affected this summer”, to be chaired by Saxton, to ensure new requirements are working, refine arrangements where needed and ensure direct and regular communication.
That will meet for the first time in January, and will discuss any additional measures for 2024.
Pearson and OCR bosses will be on that panel, Dr Saxton confirmed.
Elsewhere, exam boards will be required to have a term-time check point with centres, likely to be in June but also to be confirmed in consultation with sector leaders, to ensure any missing units are established early enough.
Bespoke training for exams officers, administration staff and any academic staff that would like it will also be carried out, as well as a requirement for improved communications from awarding bodies, including a duty to have a senior contact point with a mobile phone number.
Dr Saxton told FE Week that the plan will be “a proof of concept that these new systems will work” and that, while more work is needed on investigating the causes of the problems, the package of measures provides “a good sense” of those causes it has found so far.
“My priority, once we understood the scale of this, has focused on the things that need putting in place for 2023 to protect students against this happening again,” Dr Saxton said.
“In terms of the root causes, I want to take a bit longer to understand that and be sure we are putting the right things in place.”
On the improvements, she added: “We are really conscious of not wanting to create any additional workload for anyone. Our overall strategic aim, apart from protecting students from this risk, is to not create any new or additional workload, but to try and frontload the workload or at least break it up throughout the year so it isn’t all over 24 hours during non-term time.”
Any future sanctions on Pearson and OCR will come later on in the process.
Dr Saxton also said that the bosses at both awarding bodies had been receptive and co-operative through the process.
In the meantime, as part of the continuing work on establishing the causes of the issue, Ofqual is keen to gain evidence from students and their parents affected by the issues.
But Dr Saxton said Ofqual had heard from “surprisingly few” students and parents so far, which is another reason more time is needed to hear from more. It was also more complicated to work out how many students were affected than initially expected, Ofqual said.
Ofqual’s portal for hearing from those affected remains open. Centres can take part here while students and parents can email discussions@ofqual.gov.uk.
The task group membership is as follows:
Dr Jo Saxton (Ofqual, chief regulator) (Chair)
Catherine Sezen (Association of Colleges, interim director of education policy)
Dr Anne Murdoch (Association of School and College Leaders, senior advisor, college leadership)
Steve Rollett (Confederation of School Trusts, deputy chief executive)
Jenny Oldroyd and/or Stuart Miller (Department for Education, qualificationas directors)
Tom Bewick (Federation of Awarding Bodies, chief executive)
Ian Morgan (Joint Council for Qualifications, chairman)
Sarah Hannafin (NAHT, senior policy advisor)
Jugjit Chima (National Association of Examinations Officers, chief executive)
Jill Duffy (OCR, chief executive)
Freya Thomas-Monk (Pearson, SVP qualifications and training)
Bill Watkin (Sixth Form Colleges Association, chief executive)
16 to 19-year-olds in England study an unusually small number of subjects compared with young people in many other countries. In this context, a British Baccalaureate, broadening the scope of young people’s education to unlock economic growth is a natural policy for Rishi Sunak to be considering.
There are few details available as to how it would work in practice, but one component that has been trailed is the continued study of English and maths in the 16-19 phase. This is a positive ambition, but there are real concerns as to whether there are anywhere near enough qualified teachers to deliver this.
It is not just a teacher supply issue either. There are stark statistics from the Department for Education showing that well over a hundred thousand students each year are obliged to continue study towards GCSE or functional English and maths qualifications, having not achieved a grade 4 or above at school.
This is a large proportion of the 16-19 population, most of whom do not improve upon their original result. Raising English and maths proficiency should be a priority, but one that may prove difficult without first addressing the inequalities that exist in earlier phases of education.
Our latest research, published today, shows that pupils from an economically disadvantaged background were more likely to be behind in English and maths during school and that this was exacerbated during the pandemic.
Those in long term poverty were struggling the most, so more targeted support to help these students prior to their GCSEs is needed to create a more level playing field when students enter post 16 education. We cannot expect increased maths and English provision in the 16-19 phase to fix deep-rooted issues that were already present several years earlier.
The next general election is a little more than two years away at most, meaning there are no guarantees that these policy proposals will come to fruition, and the debate around specifics could be purely academic. However, the need to cultivate a system that provides a suitable, stretching route through sixth form or college for all students, regardless of background, must be a priority for current and future governments. The plans for a British Baccalaureate announced so far do not provide sufficient detail to conclude that this is the case.
Our research brings into sharp focus how far away we are from this ambition.
Students from economically disadvantaged backgrounds were more than three grades behind their peers across their qualifications taken during 16-19 study, rising to more than four grades when we examine the gap for those in long term poverty. These gaps are the widest they have been since 2017, when we first produced these key measures of social mobility.
2021 was no ordinary year in education, so these findings reflect the impact of school and college closures, differential learning loss and the impact of teacher assessed grades on top of gaps that already existed in 2019.
We found striking differences between students entering A levels and applied qualifications such as BTECs. Although results increased for most qualifications during the pandemic, A level grades increased the most, with students opting for applied qualifications falling almost a whole grade behind students of similar ability taking A levels, since 2019.
When A level and applied students of a similar ability were competing against each other for higher education places, the academic students would have appeared the better candidates on average. There are no two ways to look at it, this was unfair. As disadvantaged students are underrepresented among A level entrants, these differences were one of the key factors behind the widening of the disadvantage gap in 2021.
However, our research suggests that this was not the only reason that the disadvantage gap in 16-19 education widened.
Our findings show that poorer students suffered particularly in 2021, under the teacher assessed grading process and as the full impact of school and college closures was felt. When comparing to other students taking similar qualifications, those from poorer backgrounds still fell further behind.
A 16-19 Baccalaureate, introduced in the right way, could be a positive policy change, but these grand sounding announcements are not a substitute for providing sufficient support to sixth forms and colleges, especially for their most vulnerable or disadvantaged students who have fallen so far behind during the pandemic. Based on the lack of additional funding for these settings in the recent Autumn Statement, this appears to be something the government has forgotten.
AQA have acquired Training Qualifications UK, it has been announced, in a deal which will see it seek to re-establish itself in the vocational awarding market.
The takeover will see all of TQUK’s awarding, international and end-point assessment functions, worth £3.5 million in the 2021/22 financial year, transfer to the awarding giant in a move which AQA described as “a major step into vocational qualifications.”
TQUK has just shy of 290 qualifications on offer from level 1 to level 6 in a range of sectors including health and social care, leadership and management, education and hospitality.
It received EPA approval in 2017 and currently offers EPA services for 29 standards, according to the latest register of end point assessment organisations.
Ofqual’s latest vocational qualifications data puts TQUK and 10th in the ranking of the number of certificates awarded between October 2021 and September 2022 having made 105,180 awards over that period. AQA was ranked 13th over that period having awarded 81,170 certificates.
The acquisition will boost the presence of AQA in the vocational education and training market, as it is currently better known for its GCSE and A level offering.
FE Week understands AQA have been exploring acquisitions in the vocational awarding sector for some time.
Andy Walker, managing director of TQUK, said the staff team, which stood at 65 according to TQUK’s latest accounts, will remain in place. Walker said:
“Our customers will experience the same world-class service and dynamic approach to EPA and awarding they have come to expect from us, at the same time as benefitting from all of the opportunity this partnership will bring. Our team will remain in place, invigorated and committed to progress that will benefit our centres, training providers, learners and apprentices.”
AQA described the acquisition as a “keystone” in its ambition to diversify and reach more learners.
Colin Hughes, chief executive at AQA, said: “This is an exciting step for AQA, and for TQUK, bringing together our standing and expertise in assessment with a dynamic and fast-growing vocational provider. The acquisition puts a keystone into AQA’s plan to deliver more high-quality assessments to a wider range of learners.
“We look forward to working together and combining our assessment, research, talent, and technology expertise to enhance and expand the offering to more students.”
The disadvantage gap among 16-to-19-year-old students widened further in 2021, with those on applied general qualifications faring worse than during the first year of Covid-19, an influential think tank has found.
The Education Policy Institute has today published a report assessing how Covid-19 disruption impacted disadvantaged groups of students in 2021.
The disadvantage gap for 16-to-19 students widened in both 2020 and 2021, and researchers say those taking applied general qualifications fell behind their peers studying A-levels.
The report said that for 2019/20 much of the teaching for courses was completed by March 2020, when the pandemic first hit the UK, with assessment for academic qualifications like A-levels more disrupted than applied or vocational qualifications.
But 2021 saw a greater disruption to learning with assessments across all routes “affected severely”, the EPI said.
Its study found that A-level results were around 0.6 grades higher per qualification in 2021 than on 2019, while applied generals results increased by 0.4 grades.
It reported that those completing applied generals fell 0.9 grades behind their peers doing A-levels in 2021, putting students at “a relative disadvantage when competing for higher education places”.
The EPI report said students from disadvantaged backgrounds – those who claimed free school meals in any of the six years prior to finishing key stage 4 – were on average 3.1 grades behind their non-disadvantaged classmates, compared to 2.7 grades in 2019.
For those considered “persistently disadvantaged” (those claiming free school meals for 80 per cent or more of their time in education up to 16) the gap between them and their better off peers is now more than four grades.
The report said: “Unlike in 2020, the widening of the gap in 2021 could not be explained entirely by the fact that disadvantaged students were less likely to take the qualifications with greater grade increases, such as A-levels.”
While unable to conclusively say whether this was due to changes to assessments in 2021 or whether disadvantaged students were impacted more by the loss of learning, the report said it was “likely that differential learning loss was playing a part”.
Furthermore, researchers found that “since 2019, A-level grades increased at 1.7-times the rate of applied general qualification grades”.
The study said the widening of the 16-to-19 gap “reinforces the need for more support” targeted at those students.
Emily Hunt, associate director at the EPI, said: “It’s concerning that the disadvantage gap has now grown in the 16-to-19 phase of education for the previous two years, having remained relatively stable in the two preceding years.”
She added that “unless wider social and economic policy can help halt this increase in persistent and deep poverty,” it will be tough to deliver the social mobility the government says it wants.
The EPI has called for an uplift in funding for disadvantaged students, including with the introduction of a student premium in 16-to-19 institutions akin to the school pupil premium, based on previous free school meal status.
In addition, the EPI says centrally-held data that links family income to student attainment needs to be more readily available in the national pupil database to help colleges, schools and sixth forms identify disadvantaged students and target support better.
It has also called for a child poverty strategy and further research on student absence and wellbeing.
David Hughes, chief executive of the Association of Colleges, said that student poverty and disadvantage are “now at crisis levels”, warning that the AoC had “consistently highlighted the many ways that disadvantage and funding reductions have combined to widen existing achievement gaps”.
He welcomed the calls for a student premium fund, and said it was “vitally important” to increase both the overall 16-to-19 funding and targeted support to disadvantaged students.
Julie McCulloch, director of policy at the Association of School and College Leaders also called for pupil premium to be reformed to allow students up to 19.
She added: “The government must urgently address the underfunding of post-16 education, which has resulted in a reduction in student support services at a time when they’re most needed, and placed schools and colleges in an incredibly difficult position.”
A spokesperson from the Department for Education said it was investing an extra £2 billion each year for the next two years in schools, and had increased pupil premium funding for schools by £2.6 billion this year.
The spokesperson added: “To catch up we introduced our education recovery programme, with over two-million high-quality tutoring courses underway.”
The government provided additional funding for 2020/21 and 2021/22 – the 16 to 19 tuition fund – to help schools, colleges and other post-16 providers mitigate the disruption to learning from the pandemic, as well as additional funded hours.
For most secondary students, interaction with mathematics involves progression through the standard math curriculum — typically the higher-level sections of algebra, geometry, trigonometry, precalculus, statistics, and calculus. Students who enjoy challenge and variety sometimes participate in a math club, math circle, or competition team. These extracurriculars typically provide participants with the opportunity to individually solve problems in search of a correct answer, though certain supportive classroom and competition settings allow students to work together to address harder, more complex questions that require teamwork. Many of my students have successfully pursued degrees and careers in various science, technology, engineering, and mathematics (STEM) fields. Unfortunately, few of them actually use mathematics to determine a best course of action or to educate themselves about a non-STEM topic until they begin professional internships or careers.
Though I have taught and coached competition mathematics for over 16 years, my previous 15-year career as a control systems engineer found me working with and learning about optimization of locomotive fuel consumption, signal switching at television networks, air traffic path planning, and DVD manufacturing, among other applications. These experiences prefigure my goal that students learn about other fields besides mathematics, consider math’s applicability as a decision-making tool, and talk to each other in the process.
While it is possible to create small labs and explorations in the traditional math sequence that let students work toward these goals, SIAM’s MathWorks Math Modeling Challenge (M3 Challenge) [1] implements this on a larger scale. When I first learned about M3 Challenge, I reached out to some of my strongest students who enjoyed mathematics, were omnivorous in their interests, and could write and communicate effectively. The annual contest also inspired me to begin the process of launching a math modeling culture at my high school, the Emma Willard School in Troy, New York.
Apart from student curiosity and persistence, I have identified three important prerequisites for launching a math modeling culture in high school: a thorough understanding of the general process, competency with a basic tool set, and a multitude of interesting problems on which to work.
Although I spent the first part of my professional career developing mathematical models of dynamic systems, I was initially unsure where to begin in teaching the process. The Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) report[2] and SIAM’s math modeling handbooks[3] (all free to view and download) helped me create a walk-through for my students. I would also highly recommend notes from the 2019 SIAM-MfA Math Modeling Workshop[4] for high school teachers, which draw on and distill these materials. All high school students are capable of browsing the internet to obtain information on unfamiliar topics, and Google’s suite of collaborative tools facilitates collective contribution to a problem’s initial mind mapping. While I do teach basic spreadsheet use for function exploration and data analysis in precalculus, I developed short workshops to familiarize my M3 Challenge teams with the processes of creating more complex formulas and charts and using random functions to simulate outcomes. I have also begun teaching MATLAB, which I particularly enjoy as it is a technology bridge that spans my careers. Because M3 Challenge is only open to juniors and seniors (sixth form students age 16-19 in the UK), I ask experienced seniors to provide new team members with a summary of their participation by breaking down, researching, analyzing, developing, quantifying assumptions for, and validating their model from the prior year.
What makes this all “real,” of course, is finding motivating problems on which to practice. These problems should be topical and real; it is even better when they touch on subjects about which the teacher can cheerfully admit to knowing very little! One of the nicest aspects of M3 Challenge is that both past competitions and the website[5] provide numerous different problems, all of which comprise a multilayered “story” whose relevance extends beyond the competition. One of my students who participated in this year’s contest[6] praised the topic’s real-world relevance. “I knew absolutely nothing about electric trucks and very little about charging stations before this experience,” she said. “I really enjoyed being able to apply my math skills while learning about new topics. Although at times the amount of data felt overwhelming, it was so rewarding to see all of our observations and calculations come together in the final product. I will definitely be keeping tabs on the evolution of vehicles and their environmental impact in the future.”
Take two minutes to experience moments from the 2022 M3 Challenge final event in NYC!
While my school’s teams have yet to make it beyond the second round of competition, student response has been remarkably positive. “Being able to apply the knowledge I’ve gained from my math classes to a real-world scenario really interested me, especially given that there wasn’t one concrete answer to each question,” another student said. “We could really apply the organizational and math modeling skills—as well as the communication and collaboration skills—that we used during this process to any field or numerical situation.”
The contest’s benefits seemed so clear that I suggested that Emma Willard offer a semester-long, project-based course in mathematical modeling for seniors, accessible to any student who has completed precalculus or an advanced algebra course that focused on functions. The course plan, which I developed with several colleagues, introduces students to the use of models to capture the behavior or most important aspects of a messy, real-world problem with many contributing factors. The class’s inaugural semester was set for the fall of 2020.
After introducing the basics of the modeling process, the course would allow students to practice defining problems, researching contributing factors, quantifying their assumptions, and developing and testing models. It would also emphasize quantitative writing and oral presentation skills, as these are important components of any high school curriculum or professional setting.
The class would culminate in an individual project that each student chooses for herself, with guidance from the instructor. Students were to decide whether experimental or empirical modeling is most appropriate for their problem and select from model types that correspond with both the problem and their level of mathematical experience. For some, the projects would bring depth and relevance to second-year algebraic models, such as those originating with exponential, power, sinusoidal, and logarithmic functions. Difference equations, smoothed polynomial or spline models, and probabilistic simulations would provide additional depth and challenge for students who have completed a year of calculus. Most (if not all) participants would already be familiar with Desmos or GeoGebra from earlier courses, and the plan was to teach and extend existing knowledge of spreadsheets. We hoped to even include MATLAB or Python if enough students had coding experience. As developers of a new course, the teachers would be learning from their initial model and changing it to incorporate novel data as it became available. While the plan was to utilize GAIMME-based rubrics to assess student models, there was an expectation that the process would require patience, critical thinking, and a willingness to regularly amend small details as necessary.
With the right team and the right attitude, 14 hours of math modeling can still include moments that are as fun as a slumber party. Photo courtesy of Alexandra Schmidt.
COVID changed everything in terms of the math modeling course plans. Our school closed in March 2020 like many other schools, and when school resumed in fall 2020 it was VERY different. The school rejiggered all year-long courses to be semester-long courses—it wasn’t a ringing success, but the goal was to limit students to no more than three classes a semester so that if we had to go online again students would not be dealing with videos and online learning for six classes, which was pretty miserable at the end of 2019-2020. Classes that were planned one-semester classes, including the new math modeling course, were cut altogether—despite having a curriculum, approval, etc. This has been the situation for the past two years.
What I have worked to do is to incorporate more math modeling into my precalculus and first- and second-year calculus courses. It has not been nearly as systematic or tool-focused as what we proposed in our curriculum, but it has still been rewarding. Students have said, “this made me feel like a real mathematician” and “this helped me draw on modeling skills I didn’t know I had.” It is definitely not the same, or as sustained, as the math modeling course planned prior to COVID, but this is where we are at this point (December 2022).
As a final note, I want to share the very specific experience of teaching math modeling to young women (Emma Willard is an all-girls’ high school). As one of my students observed, “an all-female team like ours is a rarity, and we have created a special sisterhood.” Despite the intensity of working within M3 Challenge’s regulated time window—which gives participants 14 hours in which to educate themselves on an unfamiliar topic and produce a substantive paper—my students found the process motivating, stimulating, and even empowering. By practicing regularly before the competition, the team developed a collaborative and supportive bond and became comfortable sharing and challenging each other’s ideas. As I stopped by during Challenge weekend to bring the competing students fancy coffee drinks and baked goods and laugh with them during “vibe checks,” I was struck by both the productivity and camaraderie in the room. At the end of the day, my students came away from M3 Challenge with an enhanced sense of math’s applicability to their future studies.
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Acknowledgments: Special thanks to Caroline Albert, Laszlo Bardos, Judy Price, Chiara Shah, and Yoosong Song for their input and reflections.
Alexandra Schmidt has been a mathematics teacher at the Emma Willard School since 2014. She has taught mathematics at every level from fifth to 12th grade, prior to which she was an electrical engineer. Schmidt holds a Master of Arts in Teaching from Clarkson University and is a National Board Certified Teacher.
Traineeships make a difference to young people, with research showing participants are more likely to be in a positive destination like an apprenticeship or further learning. They consist of things you’d expect in a good education and training programme, like work preparation and experience. We’ve shown how occupational traineeships at Hartlepool College and Intertrain have helped young people prepare for jobs in construction and rail.
On the face of it, then, isn’t it a mistake to end traineeships as a national programme? Yes, the government has missed its targets to treble numbers and returned unspent money to the Treasury. But isn’t the answer to better promote traineeships and provide more incentives and support to employers and young people, particularly given better funded programmes like Kickstart will have affected take-up?
As it happens, I think the government is right. To understand why, we need to step back to first principles.
What are we trying to achieve? Our aim is to reduce the number of young people who are not in education, employment or training. This stands at around 700,000, down since the pandemic but still too high.
Lots of organisations are trying to engage these young people, including Jobcentre Plus (for those aged 18-24), councils, colleges and independent training providers. They do great work, but I think the lack of a joined-up plan and clear offer can hold us back. Too often funding rules make us think in silos about programmes that risk requiring young people to fit around policy rather than vice versa.
And the multitude of programmes, often with overlapping rules and eligibility criteria, can make it difficult to see the wood for the trees.
Surely it’s better to work with young people to agree what’s most likely to help them into education, apprenticeships or employment? Which is actually what the government says it’s trying to do.
Instead of being a relatively small standalone national programme, helping about 15,000 people a year, the money for traineeships will be rolled into the budgets for 16-19 study programmes and the adult education budget. If providers think traineeships, or elements of them, are the best support for particular groups then they can do them.
But there’s a few things to watch out for.
First, I’d like this to be the first step on a path to simplification. Could Bootcamps be next? What’s our ultimate ambition? For example, the Local Government Association argued for a single pot of money underpinned by agreements on the outcomes this would deliver and then freedom in how these would be delivered. Can we reduce the number of funding pots colleges and training providers have to deal with, with a greater focus on education and work outcomes?
Second, we’ve long argued for a Youth Guarantee, ensuring every young person is offered a job, training place or apprenticeship. That would require local and national government to work together with providers on a joined-up plan – making sure young people get referred to the right support for them regardless of which bit of the system they engage with.
Third, we need to make sure that in making this switch we don’t lose great provision or providers that are delivering fantastic traineeships now. And we need to make sure this is a real and sustained increase in funding. We’ve already shown that higher-than-expected inflation is a stealth cut of £850 million in adult skills funding over three years. The public finances are tight, but investment in education and skills is good for the economy and social justice.
Traineeships made a difference. It’s now up to providers and devolved areas to make sure all young people get the support they need.
